Permutations when All the Objects are Distinct

How many $3-$digit numbers can be formed by using the digits $1$ to $9$, if  no digit is repeated?

Six candidates are called for interview to fill some vacant posts in an office. Assuming that each candidate is fit for each post, determine the number of ways in which four posts can be filled.

How many $3-$digit numbers can be formed from the digits $1, 2, 3, 4$ and $5$, if repetition of digits is not allowed?

Find the value of $P(4, 3)$.

If ${}^{12}{P}_r{=}^{11}{P}_6+6{\times }^{11}{P}_5$, then $r$ is equal to

In how many ways can $5$ girls and $3$ boys be seated in a row so that no two boys are together? (Express your answer as only numerical value)

How many $6$-digit numbers can be formed from the digits $0,1,3,5,7$ and $9$ which are divisible by $10$ and no digit is repeated?

How many words (with or without dictionary meaning) can be made from the letters of the word MONDAY, assuming that no letter is repeated, if

           $C_1$                                                                            $C_2$

$\left(a\right)$ $4$ letters are used at a time                                         $\left(\mathrm{i}\right)$ $720$ 
$\left(b\right)$ All letters are used at a time                                       $\left(\mathrm{ii}\right)$ $240$
$\left(c\right)$ All letters are used but the                                          $\left(\mathrm{iii}\right)$ $360$
first is a vowel 

If ${}^{n+5}\mathrm{P}_{n+1}=\frac{11(n-1)}{2}{·}^{n+3}{\mathrm{P}}_n$, then the values of $n$ are

The no. of different signals that can be made by $5$ flags from $8$ flags of different colours is

If the total number of $4$digited numbers using $1,2,3,4,5,6$ divisible by $4$ with repetition is $x$ and number of $4$ digited numbers using $0,1,2,3,4,5$ divisible by $4$ with repetition is $y,$ then the value of $x, y$ are respectively-

We have to form different words with the letters of the word INTEGER. Let $m_1$ be the number of words in which $\mathrm{{\rm I}}$ and N are never together and $m_2$ be the number of words which begin with I and end with R, then $\frac{m_1}{m_{2\mathrm{ }}}$ is equal to

How many words can be made from the letters of the word INSURANCE, if all vowels come together

P, Q, R and S have to give lectures to an audience. The organizer can arrange the order of their presentation in

Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4 and then men select the chairs from amongst the remaining. The number of possible arrangements is

In a circus there are $10$ cages for accommodating $10$ animals. Out of these $4$ cages are so small that $5$ out of $10$animals cannot enter into them. In how many ways will it be possible to accommodate $10$ animals in these $10$ cages.

There are $n$ white different and $n$ black different balls marked $1, 2, 3... n$. The number of ways in which we can arrange these balls in a row so that neighbouring balls are of different colours is

The number of permutations by using all the letter of the word MONDAY, which are not beginning with M and not ending with Y is

The total number of ways of dividing $15$ different things into groups of $8, 4$ and $3$ respectively is

How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?